ASSIGNMENT STATISTICAL INFERENCE

Q1 It has been found from experience that the mean breaking strength of a brand of thread is 500 gms, with a s.d of 40 gms. From the supplies, received during the last month, a sample of 16 pieces of thread was tested which showed a mean strength of 450 gms. Can we conclude that the thread supplied is inferior? Q2 A telephone companys records indicate that individual customers pay on an average Rs 155 per month for long- distance telephone calls with standard deviation Rs. 45. A random sample of 40 customers bills during a given month produced a sample mean of 160 for long-distance calls. At 5% significance, can we say that the companys records indicate lesser mean than the actual. Q3 A car manufacturer claims that its new car gives a mileage of at least 10 kms. Per litre of petrol. A sample of 10 cars is taken, and their mileage recorded as follows (in km.p.l) 11.2 10.7 11.3 11.0 10.8 10.7 10.6 10.6 10.7 10.4 Is there any statistical evidence to support the claim of the manufacturer about mileage of its car? Q4 A machine produced 20 defective articles in a batch of 400. After overhauling it produced 10 defectives in a batch of 300. Has the machine improved? Q5 A sample of 100 tyres is taken from a lot. The mean life of tyres is found to be 39,350 kms with a standard deviation of 3,260. Could the sample come from a population with mean life of 40,000 kms? Q6 A sample of 6,400 Englishmen has a mean height of 67.85 inches and a standard deviation of 2.56 inches, while a sample of 1600 Austrians has a mean height of 68.55 inches and standard deviation of 2.52 inches. Do the data indicate that the Austrians are on an average taller than the Englishmen? Q7 In a village A out of a random sample of 1,000 persons 100 were found to be vegetarians while in another village B out of 1,500 persons 180 were found to be vegetarians. Do you find a significant difference in the food habits of the people of the two villages? Q8 A car manufacturer is procuring car batteries from two companies. For testing whether the two brands of batteries, say A and B, had the same life, the manufacturer Collected data about the lives of both brands of batteries from 20 car owners-10 using A brand and 10 using B brand. The lives were reported as follows: Lives in Months Battery A: 50 61 54 60 52 58 55 56 54 53 Battery B: 65 57 60 55 58 59 62 67 56 61 Test whether both the brands of batteries have the same life?

Q9 Five salesmen were imparted a one week specialized training for improving their selling skills. The following data was recorded during the month preceding the training and the month after the training relating to their sales per month. Can we conclude that the training has made any significant impact? Before (Rs in lakhs) 5 6.2 5.4 4.5 5.6 After (Rs in lakhs) 5.5 7 5.6 5.5 6.6 Q10 From a hospital record, the following data was obtained about the births of new born babies on various days of the week during the past year: Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total 184 148 145 153 150 154 116 1050 Can we conclude that the birth of a child on any day of the week is equally likely? Q11 A company is interested in determining whether an association exists between the commuting time of their employees and the level of stress-related problems observed on the job. A study of 116 assembly line workers revealed the following: Stress Commuting Time High Moderate Low Under 20 min 9 5 18 20-50 min 17 8 28 Over 50 min 18 6 7 At 1% level of significance check if there is any evidence of a significant relationship between commuting time and stress? Q12 A random sample of boots worn by 40 combat soldiers in a desert region showed an average life of 1.08 years with a standard deviation of 0.05. Under the standard conditions, the boots are known to have an average life of 1.28 years. Is there reason to assert at a level of significance of 0.05 that use in desert causes the mean life of such boots to decrease? Q13 The policy of the Suburban Transit Authority is to add a bus route if more than 55% of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 42 (60%) would use a proposed route from bowman park to the downtown area. Does this meet the S.T.A criterion? Use .05 significance level. Q14 Suppose that in past years the average price per square foot for warehouses in the United States has been $32.28. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 19 warehouses that are for sale across the United States and finds that the mean price per square foot is $31.67, with a standard deviation of $1.29. If the researcher uses a 5% level of significance, what statistical conclusion can be reached? What are the hypotheses? Q15 Is the type of beverage ordered with lunch at a restaurant independent of the age of the consumer? A random poll of 309 lunch customers is taken, resulting in the following contingency table of observed values. Use alpha=.01 to determine whether the two variables are independent. Preferred Beverage

Coffee/tea 21-34 26 Age 35-55 41 > 55 24

Soft drink 95 40 13

Other 18 20 32

Q16 In manufacturing, does worker productivity drop on Friday? In an effort to determine whether it does, a companys personnel analyst randomly selects from a manufacturing plant five workers who make the same part. He measures their output on Wednesday and again on Friday and obtains the following results. Worker Wednesday Output Friday Output 1 71 53 2 56 47 3 75 52 4 68 55 5 74 58 Do the samples provide enough evidence to show that productivity drops on Friday at alpha=.05? Q17 An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is $5,000. After introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was $4,800 with a standard deviation of $1,300. Does it appear the prevention plans were effective in reducing the mean amount of a claim? (use .05 significance level.) Q18 One of the new thrusts of quality control management is to examine the process by which a product is produced. This approach also applies to paperwork. In industries where large long-term projects are undertaken, days and even weeks may elapse as a change order makes its way through a maze of approvals before receiving final approval. This process can result in long delays and stretch schedules to the breaking point. Suppose a quality control consulting group claims that it can significantly reduce the number of days required for such paperwork to receive approval. In an attempt to prove its case, the group selects five jobs for which it revises the paperwork system. The following data show the number of days required for a change order to be approved before the group intervened and the number of days required for a change order to be approved after the group instituted a new paperwork system. Before: 12 7 10 16 8 After: 8 3 8 9 5 Use alpha = .01 to determine whether there was a significant drop in the number of days required to process paperwork to approve change orders. Q19 A national youth organization sells six different kinds of cookies during its annual cookie campaign. A local leader is curious about whether sales of the six kind of cookies is equally likely. He randomly selects the amounts of each kind of cookies sold and combines them into the observed data as follows: Kind of cookie Observed Frequency

189 168 155 161 216 165

Use alpha=.05 to determine whether the data indicate that sales for these six kinds of cookies is equally likely. Q20 According to a study conducted for Gateway Computers, 59% of men and 70% of woman say that weight is an important factor in purchasing a laptop. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly high proportion of women than men believe that weight is an important factor in purchasing a laptop. Use 5% level of significance.